Neuromorphic computing implemented with spiking neural networks (SNNs) based on volatile threshold switching is an energy‐efficient computing paradigm that may overcome future limitations of the von Neumann architecture. Herein, threshold switching in oxyvanite (V3O5) memristors and their application as a leaky integrate‐and‐fire (LIF) neuron are explored. The spiking response of individual neurons is examined as a function of circuit parameters, input pulse train, and temperature and reveals a pulse height‐dependent spike rate in which devices exhibit excitatory spiking behavior under low input voltages and protective inhibition spiking under high voltages. Resistively coupled LIF neurons are shown to exhibit additional neural functionalities (i.e., phasic, regular and adaptation, etc.) depending on the input voltage and circuit parameters. The behavior of both individual and coupled neurons is shown to be described by a physics‐based lumped element circuit model, which therefore provides a solid foundation for exploring more complex systems. Finally, the performance of a perceptron SNN employing these LIF neurons is assessed by simulating the classification of image recognition algorithm. These results advance the development of robust solid‐state neurons with low power consumption for neuromorphic computing.